Page 193 - Computational Colour Science Using MATLAB

180 MULTISPECTRAL IMAGING

Figure 10.8 Target (solid lines) and predicted (dotted lines) spectral reflectance factors
computed using Equation (10.21) for six samples

but estimates of p are likely to be wildly inaccurate. Figure 10.8 shows the
predicted reflectance spectra for six samples using this method.
If we use the a priori knowledge of the smoothness of reflectance spectra, then
the problem may be better constrained and more accurate predictions may be
possible. The a priori knowledge is represented by the basis functions. So, for
example, if we use a linear model with three basis functions, then the 316n
matrix of reflectance spectra P in Equation (10.20) can be replaced by Ba, where
B is a 3163 matrix of basis functions and A is a 36n matrix of coefficients to
produce Equation (10.22),

T ¼ MBA. ð10.22Þ
MB is a 363 matrix and therefore Equation (10.22) now represents a linear
system with three constraints and three unknowns and can be easily solved using
Equation (10.23),
1
A ¼ðMBÞ T. ð10.23Þ